It won't quite work as written. what I'd do is:
Round 1:K2tog K2, then follow regular round 1 (118 at beginning, 98 at end)
Round 2: K2tog, K1, then follow regular round 2 (98 at beginning, 78 at end)
Round 3:K2tog, then follow regular round 3 (78 at beginning, 58 at end)
Round 4: K1, then follow regular round 4 (58 at beginning, 39 at end)
Round 5: K1, then follow regular round 5 (39 at beginning, 20 at end)
Then you can either do another round of K2tog all around and pull through remaining ten stitches or kitchner stitch the remaining 20 stitches or whatever finishing technique you usually use for hats.
I think the math works and the decreases should line up correctly I hope :?? but you may have to play with it a little. Your 118 stitches is 2 stitches short of the right number to divide into all the decrease rounds so you have to do a little refiguring on those 4 extra stitches you added.